3. The WACC Approach

Alternatively, we can reflect the firm's interest tax savings directly in the cost of capital and use the so-called Weighted Average Cost of Capital (WACC) instead of (\( k_A \)) as the discount rate for the firm's free cash flows. The WACC is defined as follows:

  

WACC = \( k_D^* \times (1- \tau_C) \times (\frac{D}{D+E})^* + k_E^* \times (\frac{E}{D+E})^* \)

 

\( k_D^* \)

Cost of debt under the target capital structure;
\( k_E^* \)

Cost of equity under the target capital structure;
\( (\frac{D}{D+E})^* \)

Amount of debt in the firm's target capital structure.This fraction should be computed, in principle, with market values;
\( (\frac{E}{D+E})^* \)

Amount of equity in the firm's target capital structure;
\( \tau_C \)

Corporate tax rate the firm would save by claiming the interest tax deduction.

 

In the formula, the capital structure is the one the firm wants to assume for the future. Presumably, that capital structure is optimal, hence the asterisks. For example, we might want to borrow more to take advantage of more substantial tax savings.

 

Note that the cost of debt in the WACC formula is computed after corporate taxes. If the firm has to pay its debtholders an annual rate of \( k_D \) for their capital, its effective cost is only \( k_D \times(1- \tau_C ) \), since for every dollar of interest the firm pays, it saves a fraction \( \tau_C \) of that dollar in corporate taxes.

 

Under the WACC approach, firm value is computed as follows:

 

Firm value = \( \sum\frac{FCF_t}{(1+WACC)^t} \)

 

Hence, all we have to do is discount the firm's projected FCFs with the WACC. Whereas the WACC approach includes the interest tax savings in the cost of capital, the APV method adds those savings as a separate item (the DTS) in the computation of firm value.

 

What follows illustrates how we can estimate the WACC in practice. Before doing so, however, let us summarize the relevant formulae we really need (the stars indicate the possibility that we want a different, presumably optimal, capital structure) and apply the DCF-WACC approach using the example from the previous section.

 

\( k_A = k_D \times (\frac{D}{D+E})+k_E \times (\frac{E}{D+E}) \)

WACC = \( k_D^* \times(1- \tau_C ) \times (\frac{D}{D+E})^*+k_E^* \times (\frac{E}{D+E})^* \)

 

Moreover, it can be shown that WACC can also be computed as follows:

 

WACC = \( k_A-k_D^* \times \tau_C \times (\frac{D}{D+E})^* \)

 

In the previous section, we have looked at a simple firm to estimate its value using the DCF-APV approach. Our assumptions and computations have provided us with the following information:

  • Free cash flow: 4'000
  • Cost of assets, \( k_A \): 15%
  • Cost of debt, \( k_D \): 10%
  • Debt outstanding: 2'000
  • Tax rate 30%
  • Levered value of the firm: 3'530.

 

We can use this information to apply the DCF-WACC approach. To do so, note that our numbers imply a debt ratio of 56.7% (= 2'000 / 3'530). Consequently, we can use the above equation to estimate the firm's WACC:

 

WACC =\( k_A-k_D \times \tau_C \times (\frac{D}{D+E}) = 0.15 - 0.10 \times 0.3 \times 0.567 \)= 13.3%.

 

Because interest expenses are tax-deductible, the firm's after-tax cost of capital is 1.7 percentage points lower than the pre-tax cost of capital. Using the WACC of 13.3%, firm value is:

 

Firm value = \( \frac{4'000}{1.1333} \) = 3'530.

 

This is the same result as with the DCF-APV approach.